Local tame lifting for G L ( N ) . I: Simple characters

Colin J. Bushnell; Guy Henniart

Publications Mathématiques de l'IHÉS (1996)

  • Volume: 83, page 105-233
  • ISSN: 0073-8301

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Bushnell, Colin J., and Henniart, Guy. "Local tame lifting for $GL(N)$. I: Simple characters." Publications Mathématiques de l'IHÉS 83 (1996): 105-233. <http://eudml.org/doc/104111>.

@article{Bushnell1996,
author = {Bushnell, Colin J., Henniart, Guy},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {tamely ramified extensions; local tame lifting; simple type; supercuspidal representations; general linear group; irreducible representations; Hecke algebra; Iwahori-fixed vector; base change conjecture; base change map; lifting construction of simple characters},
language = {eng},
pages = {105-233},
publisher = {Institut des Hautes Études Scientifiques},
title = {Local tame lifting for $GL(N)$. I: Simple characters},
url = {http://eudml.org/doc/104111},
volume = {83},
year = {1996},
}

TY - JOUR
AU - Bushnell, Colin J.
AU - Henniart, Guy
TI - Local tame lifting for $GL(N)$. I: Simple characters
JO - Publications Mathématiques de l'IHÉS
PY - 1996
PB - Institut des Hautes Études Scientifiques
VL - 83
SP - 105
EP - 233
LA - eng
KW - tamely ramified extensions; local tame lifting; simple type; supercuspidal representations; general linear group; irreducible representations; Hecke algebra; Iwahori-fixed vector; base change conjecture; base change map; lifting construction of simple characters
UR - http://eudml.org/doc/104111
ER -

References

top
  1. [AC] J. ARTHUR and L. CLOZEL, Simple algebras, base change, and the advanced theory of the trace formula, Annals of Math. Studies, 120, Princeton University Press, 1989. Zbl0682.10022MR90m:22041
  2. [BK1] C. J. BUSHNELL and P. C. KUTZKO, The admissible dual of GL(N) via compact open subgroups, Annals of Math. Studies, 129, Princeton University Press, 1993. Zbl0787.22016MR94h:22007
  3. [BK2] C. J. BUSHNELL and P. C. KUTZKO, The admissible dual of SL(N) II, Proc. London Math. Soc., (3), 68 (1992), 317-379. Zbl0801.22011MR94k:22035
  4. [BK3] C. J. BUSHNELL and P. C. KUTZKO, Simple types in GL(N) : computing conjugacy classes, in Representation theory and analysis on homogeneous spaces (S. GINDIKIN et al., eds), Contemp. Math., 177, Amer. Math. Soc., 1995, 107-135. Zbl0835.22009MR96c:22027
  5. [BK4] C. J. BUSHNELL and P. C. KUTZKO, Semisimple types in GL(N), Preprint, 1995. Zbl0933.22027
  6. [Ca] P. CARTIER, Representations of p-adic groups : a survey, in Automorphic forms, representations and L-functions (A. BOREL and W. CASSELMAN, ed.), Proc. Symposia in Pure Math., XXXIII, part 1, Amer. Math. Soc. (Providence RI), 1979, 111-156. Zbl0421.22010MR81e:22029
  7. [Cl] L. CLOZEL, Characters of non-connected, reductive p-adic groups, Can. J. Math., 39 (1987), 149-167. Zbl0629.22008MR88i:22039
  8. [DKV] P. DELIGNE, D. KAZHDAN, M.-F. VIGNÉRAS, Représentations des algèbres centrales simples p-adiques, in Représentations des groupes réductifs sur un corps local, Hermann, Paris, 1984, 33-117. Zbl0583.22009MR86h:11044
  9. [Fl] D. FLATH, Decomposition of representations into tensor products, in Automorphic forms, representations and L-functions (A. BOREL and W. CASSELMAN, ed.), Proc. Symposia in Pure Math., XXXIII, part 1, Amer. Math. Soc. (Providence RI), 1979, 179-183. Zbl0414.22019MR81f:22028
  10. [F] A. FRÖHLICH, Local fields, in Algebraic Number Theory (J. CASSELS and A. FRÖHLICH, ed.), London, 1967, 1-41. 
  11. [Ge] P. GÉRARDIN, Weil representations associated to finite fields, J. Alg., 46 (1977), 54-101. Zbl0359.20008MR57 #470
  12. [G] G. GLAUBERMAN, Correspondences of characters for relatively prime operator groups, Canad. J. Math., 20 (1968), 1465-1488. Zbl0167.02602MR38 #1189
  13. [HC1] HARISH-CHANDRA, Harmonic analysis on reductive p-adic groups (notes by G. VAN DIJK), Lecture Notes in Math., 162, Springer, Berlin, 1970. Zbl0202.41101MR54 #2889
  14. [HC2] HARISH-CHANDRA, A submersion principle and its applications, Proc. Ind. Acad. Sci., 90 (1981), 95-102; Collected Papers, IV, Springer, Berlin, 1984, 439-446. Zbl0485.22023MR83h:22031
  15. [HC3] HARISH-CHANDRA, Admissible invariant distributions on reductive p-adic groups, in Lie theories and their applications, Queen's papers in pure and applied math., 48, Queen's University, Kingston Ontario, 1978, 281-347; Collected Papers, IV, Springer, Berlin, 1984, 371-437. Zbl0433.22012
  16. [HH] G. HENNIART and R. HERB, Automorphic induction for GL(n) (over local non-archimedean fields), Duke Math. J., to appear. Zbl0849.11092
  17. [Ho1] R. HOWE, On the character of Weil's representation, Trans. Amer. Math. Soc., 177 (1973), 287-298. Zbl0263.22014MR47 #5180
  18. [JS] H. JACQUET and J. SHALIKA, On Euler products and the classification of automorphic representations II, Amer. J. Math., 103 (1981), 777-815. Zbl0491.10020
  19. [Ko] R. KOTTWITZ, Base change for unit elements of Hecke algebras, Compositio Math., 60 (1986), 237-250. MR88e:11039
  20. [K] P. KUTZKO, The Langlands conjecture for GL2 of a local field, Ann. Math., 112 (1980), 381-412. Zbl0469.22013MR82e:12019
  21. [KM] P. KUTZKO and A. MOY, On the local Langlands conjecture in prime dimension, Ann. Math., 121 (1985), 495-517. Zbl0609.12017MR87d:11092
  22. [KP] P. C. KUTZKO and J. PANTOJA, The restriction to SL2 of a supercuspidal representation of GL2, Compositio Math., 79 (1991), 139-155. Zbl0733.22011MR92d:22027
  23. [L] R. P. LANGLANDS, Base change for GL(2), Annals of Math. Studies, 96, Princeton, 1980. Zbl0444.22007MR82a:10032
  24. [L2] R. P. LANGLANDS, On the notion of an automorphic representation, in Automorphic forms, representations and L-functions (A. BOREL and W. CASSELMAN, ed.), Proc. Symposia in Pure Math., XXXIII, part 1, Amer. Math. Soc. (Providence RI), 1979, 203-207. Zbl0414.22021
  25. [Pa] J. PANTOJA, Liftings of supercuspidal representations of GL2, Pacific J. Math., 116 (1985), 307-351. Zbl0569.22011MR86d:22013
  26. [RS] C. RADER and A. SILBERGER, Some consequences of Harish-Chandra's submersion principle, Proc. Amer. Math. Soc., 118 (1993), 1271-1279. Zbl0827.22007MR93j:22032
  27. [Ro] J. ROGAWSKI, Representations of GL(n) and division algebras over a local field, Duke Math. J., 50 (1983), 161-196. Zbl0523.22015MR84j:12018
  28. [Sa] H. SAITO, Automorphic forms and algebraic extensions of number fields, Lectures in Math., 8, Kyoto University, 1975. Zbl0381.10025MR53 #10721
  29. [Sy] P. SALLY Jr., Some remarks on discrete series characters for reductive p-adic groups, in Representations of Lie groups, Adv. Studies in Pure Math., 14, Kyoto, 1986, 337-348. Zbl0707.22007MR91g:22026
  30. [Sh] T. SHINTANI, On liftings of holomorphic cusp forms, in Automorphic forms, representations and L-functions (A. BOREL and W. CASSELMAN, ed.), Proc. Symposia Pure Math., XXXIII, part 2, Amer. Math. Soc. (Providence, RI), 1979, 97-110. Zbl0415.10019MR82e:10051
  31. [W] A. WEIL, Exercices dyadiques, Invent. Math., 27 (1974), 1-22; Oeuvres scientifiques, III, Berlin, 1980, 343-364. Zbl0307.12017MR52 #350
  32. [Ze] A. V. ZELEVINSKY, Induced representations of reductive p-adic groups II: On irreducible representations of GL(n), Ann. Scient. Éc. Norm. Sup. (4), 13 (1980), 165-210. Zbl0441.22014MR83g:22012

Citations in EuDML Documents

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  1. Laure Blasco, Changements de base explicites des représentations supercuspidales de U ( 1 , 1 ) ( F 0 )
  2. Vincent Sécherre, Représentations lisses de G L ( m , D ) I : caractères simples
  3. Corinne Blondel, Sp(2N)-covers for self-contragredient supercuspidal representations of GL(N)
  4. J.-F. Dat, Types et inductions pour les représentations modulaires des groupes p -adiques. With an appendix by Marie-France Vignéras
  5. Colin J. Bushnell, Guy Henniart, Davenport-Hasse relations and an explicit Langlands correspondence, II : twisting conjectures
  6. Colin J. Bushnell, Guy Henniart, Philip C. Kutzko, Correspondance de Langlands locale pour GL n et conducteurs de paires

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